Lattice width directions and Minkowski's 3^d-theorem

J. Draisma; T.B. McAllister; B. Nill

Lattice width directions and Minkowski's 3^d-theorem

J. Draisma, T.B. McAllister, B. Nill

Discrete Algebra and Geometry

Research output: Book/Report › Report › Academic

Abstract

We show that the number of lattice directions in which a d- dimensional convex body in Rd has minimum width is at most 3d -1, with equality only for the regular cross-polytope. This is deduced from a sharpened version of the 3d-theorem due to Hermann Minkowski (22 June 1864-12 January 1909), for which we provide two independent proofs.

Original language	English
Publisher	s.n.
Number of pages	10
Publication status	Published - 2009

Publication series

Name	arXiv.org [math.CO]
Volume	0901.1375

Cite this

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AU - McAllister, T.B.

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T3 - arXiv.org [math.CO]

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Lattice width directions and Minkowski's 3^d-theorem

Abstract

Publication series

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